# Three Positive Numbers

What three positive numbers give the same result when multiplied and added together?

### 8 guesses to Three Positive Numbers

Warning: Use of undefined constant bfa_comments - assumed 'bfa_comments' (this will throw an Error in a future version of PHP) in /home/customer/www/riddledude.com/public_html/wp-content/themes/atahualpa/comments.php on line 132
• Frank

1,2,3

• anant

1,2,3

• Frank, you are today’s winner!
1, 2, and 3.

• Margot

1,2,3

• brent

Looks like the square root of 3 would also solve this riddle if it is used as all three values.
root 3 x root 3 x root 3 = root 3 + root 3 + root 3

I don’t know how to tell if there are other solutions (other than the one Frank gave) where three unique values solve the problem? Any ideas?

• brent

O.K. I’ve found a general solution (but my inability to enter math formulae on here is a bit frustrating, I’m happy to follow-up if there is interest.

But for example,
If you assume A = square root of (11.1)
Which is approximately 3.331666

Then this is true:
A/10 + A + Ax10 = A/10 x A x Ax10
or approximately
0.3331666 + 3.331666 + 33.31666 = 0.3331666 x 3.331666 x 33.31666 = 36.98149

• brent

For some reason, this one has captured me!

Another three positive numbers that add up to their product are:
(Where B = square root of 3.5)
B/2 + B + 2B = B/2 x B x 2B

Or approximately:
0.935414 + 1.870829 + 3.741657 = 0.935414 x 1.870829 x 3.741657 = 6.5479

• brent

Oh boy, it is much easier than I had been making it out to be.

Given any two positive numbers: B & C you can find the 3rd (usually smaller) number to complete the equation:
A + B + C = A x B x C

using: A = (B + C) / (B x C – 1)

Of course, B x C – 1 must not equal 0.

I think I can get on with my life now…